where, \(\vec{A} = {a_0, a_1, a_2, ..., a_n}\)  are constant coefficients that can be used to reconstruct the PDE solution on any local subdomain. \(\vec{A}\)  can be considered as a compressed encoding of the Laplace solutions. Since, it is not possible to explicitly derive such compressed encodings for other high dimensional and non-linear PDEs, the CoMLSim approach relies on autoencoders to compute them. It is known that non-linear autoencoders with good compression ratios can learn powerful non-linear generalizations [1]}, [2]}, [3]}. Autoencoders also have great denoising abilities, which improve robustness and stability, when used in iterative settings [4]}. In their paper, [5]} demonstrate that the latent manifold established by a trained autoencoder is stable for varying intensities of Gaussian noise. This quality of autoencoders is useful for the convergence of the iterative inferencing approach.
